A statement from British Airways said: “Customers are being checked in as normal after an earlier problem was resolved. We are sorry for the temporary check-in problems, which caused some delays for our customers first thing this morning.

“This issue is now resolved and our staff are working flat out to help customers get away on their holidays.”

The airline said the IT shutdown was caused by an “uncontrolled return of power” after an outage that physically damaged servers at its data centre. It has been estimated that BA could face a £100m compensation bill.

Tourists arriving in some popular destinations have been met with immigration lines hundreds of metres long – some having to wait for up to four hours according to airline lobby groups – as staff carry out tighter counter-terror checks.

Airlines UK, an industry body representing UK-registered carriers, said it had warned the Department for Transport about the problem in May, although they were told by ministers the issue had eased.

Tim Alderslade, the body’s chief executive, said: “Clearly, the situation has changed markedly as we enter peak holiday season and it is now up to the UK government to work with industry to use whatever influence it can within the EU to persuade Schengen member states to resource their border operations properly.”

New EU rules introduced after terror attacks in Paris and Brussels require countries to carry out more stringent checks on travellers entering and leaving the Schengen area, which allows passport-free movement across much of the EU.

The change means the details of passengers from non-Schengen countries, such as the UK, are run through databases to alert authorities if they are known to pose a threat.

However, Alderslade said attempts to improve resources at border controls had “failed to happen thus far”.

Pictures on social media in recent days have shown long queues of passengers in crowded terminals.

Lobby group Airlines For Europe (A4E) said passengers arriving at airports in Spain, Portugal, France, Italy and Belgium were being forced to endure long waits to get through immigration.

The group, which represents carriers including easyJet, Ryanair and British Airways’ parent company IAG, claimed some passengers were missing their flights because of the issue.

A4E’s managing director, Thomas Reynaert, said passengers had been left “devastated”.